President Donald Trump listens as Homeland Security Secretary Markwayne Mullin speaks during a swearing-in at the Oval Office of the White House on Tuesday in Washington. (AP Photo/Alex Brandon)

WASHINGTON (AP) — Travel disruptions deepened Tuesday as senators raced to salvage a proposal to end the Homeland Security shutdown by funding much of the department, including airport workers going without pay, but excluding immigration operations that have been core to the dispute.

The sudden sense of urgency comes as U.S. airports are snarled by long security lines, with travelers being told to arrive hours before their flights in Houston, Atlanta and Baltimore/Washington International. Routine Department of Homeland Security funding was halted in mid-February ahead of the busy spring travel season. Nearly 11% of Transportation Security Administration workers who were scheduled to report for duty Monday — more than 3,200 — missed work, and at least 458 have have quit altogether since the shutdown began, according to DHS.

Democrats are refusing to fund the department without restraints on Trump’s immigration enforcement and mass deportation operations after federal agents killed two citizens in Minneapolis.

“The time to end this is now,” said Senate Majority Leader John Thune, R-S.D.

But Democrats panned the offer as insufficient. And President Donald Trump himself was noncommittal.

“I think any deal they make, I’m pretty much not happy with it,” Trump said at an event at the White House swearing in his new Homeland Security Secretary Markwayne Mullin.

Airport conditions have become increasingly unpredictable with swelling crowds seen in major hubs. Travelers headed to LaGuardia and John F. Kennedy airports in New York — as well as Newark Liberty International in neighboring New Jersey — still couldn’t check online TSA wait times Tuesday morning.

Immigration and Customs Enforcement agents were spotted in terminals, including at Philadelphia International Airport, where a protester was seen at one of the checkpoints holding a sign criticizing ICE. In Houston, passengers at George Bush Intercontinental Airport spent hours Tuesday navigating meandering security lines that twisted and turned across multiple floors.

Airport wait times listed in the MyTSA mobile app may be outdated because the agency isn’t actively updating its websites during the shutdown.

The contours of the deal emerged once a group of Republican senators met with Trump at the White House late Monday, after he upended talks and deployed federal immigration officers at certain airport security checkpoints — a move some lawmakers warned could lead to heightened tensions.

The proposal would fund most of Homeland Security, but not one main part of ICE — the enforcement and removal operations that are core to Trump’s deportation agenda.

Key to ending the standoff appears to be the senators’ ability to shift the president’s attention off his plan to link any department funding to his push to pass the so-called SAVE America Act, a strict proof-of-citizenship and voter ID bill that has stalled in the Senate ahead of the midterm elections.

The deal could provide a political exit from the standoff over the embattled Department of Homeland Security, which was created in the aftermath of the Sept. 11, 2001, attacks but has come to symbolize Trump’s aggressive mass deportation agenda, with its goal of removing 1 million immigrants this year.

Under mounting political pressure, Trump ousted Homeland Security Secretary Kristi Noem amid the public outcry over the immigration operations, and senators late Monday confirmed Mullin, one of their own, as the president’s handpicked replacement.

Mullin, an Oklahoma senator who aligns with Trump’s agenda, provides a potentially new face for the department.